where \(\mathcal {C}_m = 8 \pi \sigma _\mathrm {pr}^{2m + 3} \Gamma (m + 1/2)\) . In the presence of time-translational invariance, the infinite series on the right-hand side of Eq. (REF ) vanishes and we reproduce the equilibrium relation \(f_\mathrm {Q}^{\rm eq}( q, \tau ) = 8\sigma _\mathrm {pr} \sqrt{\pi } \int \displaylimits _{-\infty }^{+\infty } d\omega \, S^{\rm eq}( q, \omega , t)\)  [1]}. However, high-order derivative terms on the right-hand side can play a significant role far from equilibrium, as discussed in Sec. .
